PEKANBARU, Indonesia (Reuters) - Indonesia has sent nearly 21,000 personnel to fight forest fires raging in its northern islands, the disaster management agency said on Tuesday, but smoke cloaks much of the region with pollution readings in the "very unhealthy" region in neighboring Singapore.

Slash-and-burn agriculture has blanketed Singapore, Malaysia and northern Indonesia in a choking "haze" for weeks, pushing up pollution levels and disrupting flights, as it does every year. Indonesian efforts to halt the seasonal clearances have failed.

More than 135,000 Indonesians were reported to be suffering from respiratory diseases, the disaster agency said in a statement.

"Looking at the current situation, it essential for us to extend the period of state of emergency due to haze for another 14 days," said Arsyadjuliandi Rachman, acting governor of Riau province, one of the worst-hit areas.

"Our focus will remain on monitoring the health of our people."

Schools in parts of Malaysia were ordered closed for a second day on Tuesday and Singaporean commuters were wearing masks as they have for much of the last two weeks.

Indonesia has faced criticism for turning down offers of help from Singapore, even as it struggles to contain fires that have been exacerbated by a prolonged dry season.

Indonesian officials, including Vice President Jusuf Kalla, have repeatedly said they have enough resources to handle the crisis, with Kalla adding that neighboring countries should be grateful for clean air provided by Indonesia's rainforests outside the haze season.

Kalla this week toned down his earlier comments and said Indonesia was open to foreign assistance, according to media.

President Joko Widodo last week visited Central Kalimantan and called for urgent action including building canals to irrigate parched peatlands where fires can be harder to put out, media reported.

Indonesian government has launched investigations of more than 200 companies and taken legal action against just four.